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Simulation and estimation of long memory continuous time models. (English) Zbl 0836.62060

Summary: Some general properties of long memory continuous time processes are recalled or proved. Methods of simulation are studied. A comparison with the usual discrete time autoregressive fractionally integrated moving- average filter is made and illustrations are provided. Then, two methods of estimation of the parameters of such a model from a discrete sample are studied, both theoretically and empirically, with Monte Carlo experiments.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
65C05 Monte Carlo methods
62F10 Point estimation
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